the application of second order differential equation

... because of both practical and theoretical aspects There have been many papers investigating the solutions of three-point BVPs, see 2 5, 10, 12 and references therein Recently, the existence of solutions ... and the existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory Motivated by the above works, we consider the singular third-order ... known results 1 Introduction Third-order differential equations arise in a variety of different areas of applied mathematics and physics, such as the deflection of a curved beam having a constant

Ngày tải lên: 21/06/2014, 05:20

... formulation of the problem avoids the difficulties The difficulties just mentioned concern the basic formulation of the linear operator formed from the left-hand side of (1.1), together with the boundary ... that there are certain difficulties with the formulation of the problem as usually used in the literature These difficulties can be avoided by some additional conditions on the structure of the time ... C0(Tκ)) With the norm | u |1,T:= |u |0,T+uΔ  0, Tκ, u ∈ C1 these spaces are again Banach spaces To define the second derivative ofu, we define the time scaleTκ2 :=(Tκ)κ, and then the second derivative

Ngày tải lên: 22/06/2014, 22:20

... the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the ... understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. Conclusions: The second-order differential equation revealed the basic ... common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to

Ngày tải lên: 13/08/2014, 16:20

... Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics, ... that the number of basic frequencies of ˙x  ψx, t, x ∈ R, is the same as that of basic frequencies of its unique solution Trang 2The spectrum containment of almost periodic solution of equationxt ... Trang 7The expressions of x 2n , x 2n1 , y 2n , ω t, and xt are important in the process ofstudying the spectrum containment of the almost periodic solution of 1.1 Before giving the main theorem,

Ngày tải lên: 21/06/2014, 20:20

... Fredholm property of the operator In the rest of paper we use the following notations is zero matrix of order d × d and θ is zero element of d . Id : the identity matrix of order d. ν z(t) ... (3.7) and the continuity of of Lemma is complete. we can obtain the estimate (3.8) and the proof The main result is presented as below. Its proof is directly corollary of above analysis. Theorem ... 12], the pertubation method (the name was proposed by Kannan [7]) or continuation method of Mawhin [4],... One of important hypotheses of Mawhin’s continuation theorem that is the Fredholm of index zero

Ngày tải lên: 14/10/2015, 08:45

... details the reader is referred to5 10 and the references therein The BVPs on the half-line arise naturally in the study of radial solutions of nonlinear elliptic equations and models of gas pressure ... Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line 1 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China 2 Department of Mathematics ... extend and generalize the results of16,17 to some degree The main tools used in this paper are Leray-Schauder nonlinear alternative and the fixed point index theory The rest of the paper is organized

Ngày tải lên: 21/06/2014, 11:20

... Properties of Solutions of Singular Second-Order Differential Equations Irena Rach ˚unkov ´a,1 Svatoslav Stan ˇek,1 Ewa Weinm ¨uller,2 1 Department of Mathematical Analysis, Faculty of Science, ... model of1.4, Trang 3The question which we now pose is the role of the boundary conditions1.3, moreprecisely, are these boundary conditions necessary and su fficient for the solution u of 1.6 ... if the following Proof Let u be a solution of3.1 Then u satisfies 3.21, and the result follows immediately by substituting the values, u 0  c1 c0 into the boundary conditions3.26b Theorem

Ngày tải lên: 21/06/2014, 20:20

... Solutions of Singular Nonautonomous Second-Order Differential Equations Irena Rach ˚unkov ´a and Jan Tome ˇcek Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, ... In particular, by means of properties of the associated vector field ut, ptut together with the Kneser’s property of the cross sections of the solutions’ funnel, the authors provide conditions ... damped solution of problem 2.13, 1.10 Therefore, we can borrow the arguments of12 in the proofs of this section Theorem 3.3 If u is a damped solution of problem 1.1, 1.10, then u has a

Ngày tải lên: 21/06/2014, 20:20

... set of t such as those near t = 1 in the proof of Theorem 3.1 We remark that Theorem 3.2 does not assert the uniqueness of the positive solution when b = 0 In fact, in the. .. either ... least in the neighborhood of 0 before the first zero of u(t;h). It is easy to see that, in fact, z(t) = hy(t;L 1 ), where y(t;λ) is the solution of (2.8)definedintheproofofLemma 2.3. By the Sturm ... of the nonlinear term is needed are to enable us to compare the nonlinear term of (1.1) with the linear terms of the comparing equations (3.8) and (3.11)... for the study of

Ngày tải lên: 22/06/2014, 06:20

... the asymptotics of the solutions. .. n→∞ (4.10) Thus, the limiting equation is exactly the linearized equation (4.1), and an application of Poincar´ ’s theorem completes the proof of ... (1.18) Now the proof follows as the proof of [7, Theorem 1.4.8].  The next two theorems give precise information about the asymptotics of linear non- autonomous difference equations. Consider the scalar ... characteristic equation of the linearized equa- tion evaluated at the equilibrium. The results on asymptotics of (1.2), (1.3), and (1.4)will show all the complexity of the asymptotics of the general equation

Ngày tải lên: 23/06/2014, 00:20

... detailed instructions from the beginning of the thesis to the valuable comments till the end I would like to express my gratitude to all of my lecturers at faculty of post-graduate studies as ... Tourism The specific objectives of the thesis are: (1) To find out what the effects of portfolio on improving learners’ writing skill are (2) To find out what problems emerging in the application ... conduct this research with the hope that a new teaching method will benefit students, making them keen on the subject, and improving their writing skill 1.2 Objectives of the thesis This research intends

Ngày tải lên: 16/12/2017, 23:11

... INTRODUCTION 1 1 Rationale of the study 1 2 Aims of the study 3 3 Research questions 3 4 Scope of the study 3 5 Methods of the study 4 6 Significance of the study 4 7 Design of the study 5 Summary ... 157 Design of the study The study consists of three main parts: Part A – Introduction - presents the rationale of the study, the aims, the research questions, the scope, the methods, the significance ... achievement The second impetus is the existing controversies regarding the effects of feedback among reseachers The last ground is the practical hypothesis at PPC I that the application of teachers’

Ngày tải lên: 23/09/2020, 23:02

... INTRODUCTION 1 1 Rationale of the study 1 2 Aims of the study 3 3 Research questions 3 4 Scope of the study 3 5 Methods of the study 4 6 Significance of the study 4 7 Design of the study 5 Summary 5 ... of the studyThe study consists of three main parts: Part A – Introduction - presents the rationale of the study, the aims, the researchquestions, the scope, the methods, the significance and the ... achievement The second impetus isthe existing controversies regarding the effects of feedback among reseachers Thelast ground is the practical hypothesis at PPC I that the application of teachers’feedback

Ngày tải lên: 08/11/2020, 12:15

... INTRODUCTION 1 1 Rationale of the study 1 2 Aims of the study 3 3 Research questions 3 4 Scope of the study 3 5 Methods of the study 4 6 Significance of the study 4 7 Design of the study 5 Summary ... 157 Design of the study The study consists of three main parts: Part A – Introduction - presents the rationale of the study, the aims, the research questions, the scope, the methods, the significance ... achievement The second impetus is the existing controversies regarding the effects of feedback among reseachers The last ground is the practical hypothesis at PPC I that the application of teachers’

Ngày tải lên: 05/12/2020, 08:03

... STATEMENT OF ORIGINALITY This is to certify that the thesis entitled THE INFLUENCE OF THE APPLICATION OF PAPERRATER ON THE SECOND-YEAR STUDENTS' USE OF COHESIVE DEVICES IN AN ENGLISH CLASS AT THE UNIVERSITY ... HOCHIMINH CITY UNIVERSITY OF SOCIAL SCIENCES & HUMANITIES FACULTY OF ENGLISH LINGUISTICS & LITERATURE THE INFLUENCE OF THE APPLICATION OF PAPERRATER ON THE SECOND-YEAR STUDENTS' USE OF COHESIVE DEVICES ... designed for a study entitled “The influence of the application of PaperRater on the second-year students' use of cohesive devices in an English class at the University of Science, Vietnam National

Ngày tải lên: 22/04/2021, 23:37

... graduate from the college They start learning this subject from the second semester of the first year to the second semester of the second year The author’s action research occurred in the first ... and their knowledge on the use of portfolio That is how the application process began Next, the teacher presented the objectives (acounting for 30 % of their total grade) and the procedure of ... chapter, the author mentions the methodology applied to conduct the research It consits of two main parts: 1 The information about the context of the study : General information about the college, the

Ngày tải lên: 28/06/2022, 08:46

... influencing their learning success and overall achievement There are ongoing debates among researchers about the effectiveness of feedback, highlighting the complexities of its impact Additionally, the ... speaking errors made by second-year students, the feedback strategies employed by teachers to address these errors, and the students' perceptions of the feedback received from their instructors.Qualitative ... and analyzes students' attitudes towards the feedback they receive from their teachers.In the conclusion of Part C, the study summarizes key findings and offers valuable suggestions for teachers

Ngày tải lên: 28/06/2022, 10:23

... interval symmetrizes about the origin. Then, similar to the proof of (2.9), we can verify the condition f  (α) = f  (β), and the other conditions in Lemma 2.2 are satisfied all the way. Hence, it also ... contributions QZ carried out the theoretical proof and drafted the manuscript. XH participated in the design and coordination. Both of the two authors read and approved the final manuscript. References [1] ... [α, β], too. Then, by a similar method to the proof of (2.3) together with Lemma 2.2, we can obtain (2.4) immediately. For the other ordinary cases, i.e., a = 0, we only need to move the interval...

Ngày tải lên: 20/06/2014, 21:20

... while all the regularly varying solutions of index 1 are asymptotic to a positive multiple of k. On the other hand, in the remaining two cases, the study of the regular variation of the solutions ... examined by means of the contraction mapping theorem in the Banach space of sequences converging towards zero. The following properties of h will play a crucial role in the proof. The first two are ... 1 α  α−1  . 5.2 Proof. The main idea of the proof is the analogous of the linear case, apart from some additional technical problems. We omit all the details, pointing out only the main differences. Necessity Set...

Ngày tải lên: 21/06/2014, 11:20